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Stepwise change in Gibbs free energy curve observed in Si(111) DAS domain growth
Applied Surface Science 130–132 Ž1998. 18–22
Stepwise change in Gibbs free energy curve observed in Si ž111 / DAS domain growth T. Ishimaru b
a,)
, K. Shimada a , T. Hoshino c , H. Kawada a , I. Ohdomari
a,b
a School of Science and Engineering, Waseda UniÕersity, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169, Japan Kagami Memorial Laboratory for Material Science and Technology, Waseda UniÕersity, 2-8-26 Nishiwaseda, Shinjuku-ku, Tokyo 169, Japan c Faculty of Pharmaceutical Sciences, Chiba UniÕersity, 1-33 Yayoicho, Inage-ku, Chiba 263, Japan
Received 1 September 1997; accepted 26 December 1997
Abstract The formation and the annihilation rates of stacking fault ŽSF. half-units were precisely determined from the high-temperature scanning tunneling microscopy ŽSTM. observation of dimer–adatom–stacking-fault ŽDAS. domains grown on quenched SiŽ111. surface at 4858C, as a function of the number of corner holes shared by a preexisting large domain and a newly born single SF triangle. In contrast to the general nucleation and growth with a single atom as a building unit, in the nucleation and growth of a n = n DAS domain with a single SF half-unit as a building unit, Gibbs free energy as a function of the number of SF half-units has discrete values. This feature is reflected in the behavior of a newly born SF half-unit adjacent to a larger DAS domain. For the SF half-units sharing one corner hole, the formation rate was lower than the annihilation rate due to the greater contribution of periphery strain to the increase in the Gibbs free energy than that of area increase. For the formation of the SF half-unit sharing two corner holes, the annihilation rate was negligibly small, suggesting that the addition of this single SF triangle increases the domain area keeping the periphery length constant, which results in Gibbs free energy reduction. q 1998 Elsevier Science B.V. All rights reserved. PACS: 68.35.Rh; 82.60.Nh; 64.60.Qb; 82.65.Dp Keywords: SiŽ111. surface; DAS domain; Nucleation and growth; Quantized Gibbs free energy change; Formation rate; Annihilation rate
1. Introduction SiŽ111. dimer–adatom–stacking-fault ŽDAS. reconstruction is one of the most interesting subjects in surface science. Not only the most stable 7 = 7 DAS structure but also the metastable n = n Ž n:odd. DAS structures with various sizes are known to appear on )
Corresponding author.
SiŽ111. surface w1–4x. The dynamical aspects of the DAS reconstruction have been extensively studied, and many features of the DAS domain growth have been made clear w5–8x. Our high-temperature scanning tunneling microscopy ŽSTM. observation of the quenched SiŽ111. surface has shown that the single stacking fault ŽSF. half-units appeared in the disordered ‘1 = 1’ region and the DAS domain growth proceeded by adding the SF half-units one by one
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 0 1 8 - X
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
sharing a corner hole w7,8x, which has revealed that the SF half-unit is a building unit of the DAS domain growth. We have been successful also to clarify the existence of the critical nucleus size of DAS domain growth and to determine the critical nucleus size at several temperatures w9x. The temperature dependence of the critical size were explained reasonably by the Gibbs free energy change based on a simple two-dimensional nucleation and growth theory. The Gibbs free energy curve for DAS domain nucleation can be understood by the competition between the energy decrease as a function of the DAS domain area and the energy increase as a function of the boundary length between ‘1 = 1’ matrix and DAS domain. In general for nucleation and growth, the Gibbs free energy changes smoothly as the domain size increases. This is because the atom size added to a preexisting domain is much smaller than the domain size. However, in the case of n = n DAS domain growth, the size of a single SF half-unit is not negligible compared to a domain size. This fact forces us to imagine that the Gibbs free energy curve cannot be continuous nor smooth because of the one-by-one addition of the building unit. In this work, through a very large number of sequential STM observation, we have obtained the formation and annihilation rates of the SF half-unit as a function of the number of corner holes shared by a preexisting large domain and a newly born SF triangle. The results clearly revealed the stepwise increase and decrease in the Gibbs free energy.
2. Experimental The experiments were performed using high-temperature STM unit ŽJEOL 4000XV. installed in an ultrahigh vacuum chamber with a base pressure below 8 = 10y1 1 Torr. A sample with a size of 7 = 1 = 0.3 mm3 was cut from a CZ wafer with the resistivity of 5 V cm and with the off angle of 0.18. After organic chemical cleaning and 5% HF treatment, the sample was installed into the vacuum chamber, degassed at 5008C for 12 h, and flashed up
19
to 12008C until the whole area of the surface was covered with 7 = 7 phase. In order to make high-temperature STM observation immediately after the quenching, the SiŽ111. surface was kept at the observation temperature of 4858C for over 1 h in advance using a dc current supply, then rapidly heated up to 11008C and rapidly cooled down again to 4858C using another dc current supply. The STM observations at 4858C were started just a few minutes after the quenching. The sample temperature of 4858C was determined by a power– temperature relationship based on the temperatures above 6008C measured by an infrared pyrometer. All STM images were acquired with a constant height mode and at a scan rate of 8.8 srimage, and were recorded on video tapes for over 3 h.
3. Results Fig. 1 shows the growth of DAS domains on the quenched SiŽ111. surface at 4858C. On the quenched surface kept at around 4858C, both the DAS region and the disordered ‘1 = 1’ region coexist, and the DAS domain growth is slow enough to see the formation of the individual SF half-unit. In the successive STM images in Fig. 1, the SF half-units indicated by the thick lines are the ones newly added to a side of a large DAS domain with sharing of one corner hole or two corner holes. It is also noted that a SF half-unit annihilated in Fig. 1h, i. In the following, the newly born SF half-unit sharing one Žtwo. corner holeŽs. with a preexisting large DAS domain is denoted by SF1 ŽSF2.. The frequency of the formation of SF1 and SF2 were counted from more than 1000 STM images, and the formation rate of each SF half-unit was determined by dividing the total number of formations of each SF half-unit by the total existence time of the available formation sites. The numbers of the annihilation of SF1 and SF2 were also counted, and the annihilation rate of each SF half-unit was determined by dividing the annihilation number by the total existence time of each SF half-unit. The formation and annihilation rates are summarized in Table 1 together with the number of formation and annihila-
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
20
Fig. 1. Successive STM images observed at around 4858C. The images of Žb. – Ži. were taken at 9, 18, 52, 70, 88, 106, 112 and 150 s after Ža., respectively. SF half-units indicated by thick lines are the newly formed one after the previous image. A SF half-unit sharing one corner hole annihilated in Ži..
tion in parentheses. What should be noted is, for SF1, that the formation rate is lower than the annihilation rate in spite of the supercooling condition for the DAS phase to grow. For SF2, namely in the
case where a single SF half-unit is added to a domain with sharing of two corner holes, the formation rate is reasonably high and the annihilation rates are negligibly small.
Table 1 Formation and annihilation rates of SF1 and SF2 Formation rate wsy1 x Žnumber of formation. SF1 SF2
y4
6.5 = 10 Ž147. 4.9 = 10y3 Ž226.
Annihilation rate wsy1 x Žnumber of annihilation. 1.6 = 10y3 Ž24. y Ž0.
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
21
4. Discussion In the regular case of crystal nucleation and growth, a monomer, i.e., a building unit, is an atom, and the addition of individual atoms to the nucleus cannot be seen. So, the free energy curve to describe the nucleation and growth, which is given by the summation of the energy increase due to periphery increase and the energy decrease due to area increase, is regarded to be continuous and smooth. It is also noted that the nucleus is regarded to preserve the equilibrium shape. In the case of the nucleation and growth of DAS region, a SF half-unit corresponds to a monomer. The DAS domain growth takes place discontinuously by adding the SF half-unit one by one. Fig. 2a schematically shows the growth of DAS domain preserving the equilibrium shape, which was the assumption in our previous work to explain the experimentally determined temperature dependence of critical nucleus size. Fig. 2b shows the intermediate growth stages between two adjacent DAS domains in equilibrium shape cited from in Fig. 2a. In the intermediate stages, firstly, SF1 is added to a side of the DAS domain, and then, SF2 is added along the side. The number of SF2s is higher for the larger domain size, while the number of SF1 is usually only one irrespective of the domain size. The change in Gibbs free energy upon the formation of SF1 and SF2 is considered as follows. The area increment of a DAS domain is considered to be same for both SF1 and SF2. The peripheral length of the DAS domain increases by 3a Ž a is one side length of a SF half-unit. upon SF1 formation, whereas the peripheral length does not change upon SF2
Fig. 2. Schematics of Ža. DAS domain growth preserving the equilibrium triangular shape, and Žb. intermediate growth stages between the triangular shaped DAS domains in the box in Ža.. In Žb., SF1 is first added to a side of the original DAS domain, and then SF2s are added along the side.
Fig. 3. Quantized Gibbs free energy curve upon the nucleation of DAS domain. It is based on the one-by-one addition of the SF half units. The lower line is the energy decrease due to the area increase, and the upper line is the energy increase due to the periphery increase. The arrows with 1–3 correspond to those in Fig. 2b.
formation. Hence, for SF1 formation, the Gibbs free energy should increase if the energy increase due to the periphery increase is larger than the energy decrease due to the area increase. On the other hand, for SF2 formation, the Gibbs free energy simply decreases as the area increases. Fig. 3 shows the Gibbs free energy change upon DAS domain nucleation and growth on the basis of the energy change associated with ‘1 = 1’™ 7 = 7 phase transition, the data of which was used in our previous work w9x. The lower line is the energy decrease due to the area increase of DAS domain which is proportional to the number of the SF halfunit newly added to the domain. The upper line is the energy increase due to the boundary strain, which increases only when the SF1 is added to a straight side of a domain. The growth stages indicated by the numbered arrows correspond to those in Fig. 2a. It is interesting to note that the free energy curve is discontinuous. It is obvious that, for a single SF triangle to be formed, an activation energy to put more than 50 atoms in order is necessary. Fig. 4 schematically shows the process of one-by-one addition of SF half-unit in terms of energy change. The process corresponds to the one in Fig. 2a and the horizontal lines correspond to the quantized free energy values shown in Fig. 3. D Ef1 and D Ef2 in Fig. 4 are the activation energy of the SF1 and SF2 formation, and D Ea1 and D Ea2 the activation energy for the SF1
22
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
Fig. 4. Schematic diagram of the formation and annihilation processes of the SF half-units. The numbers 1–3 correspond to those in Fig. 2b and Fig. 3. D Ef1 and D Ef2 are the activation energy for the SF1 and SF2 formation, and D Ea1 and D Ea2 are the activation energy for the SF1 and SF2 annihilation, respectively.
and SF2 annihilation, respectively. For SF1 formation, due to the higher frequency of annihilation based on smaller D Ea1 than D Ef1 , the annihilation rate is higher than the formation rate as seen in Table 1. For stages 2 and 3, D Ef2 is smaller than D Ea2 because of the free energy decrease, and therefore the formation rate becomes higher than the annihilation rate, in agreement with the experimental results. These local features of Gibbs free energy change is considered to be seen in every growth stage from a triangular DAS domain to the next larger triangular DAS domain.
5. Conclusion The formation and the annihilation rates of SF1 and SF2 were precisely determined from the hightemperature STM observation of the DAS domain growth on quenched SiŽ111. surface at 4858C. The local feature of the Gibbs free energy change upon the DAS domain nucleation was investigated. For the
SF half-unit formation sharing one corner hole, it was found from the lower formation rate and the annihilation rate that the Gibbs free energy increased. For the formation of the SF half-unit sharing two corner holes, the Gibbs free energy decreased, which qualitatively agrees with the result of the far smaller annihilation rate than the formation rate. It is concluded that the discrete and stepwise feature of the Gibbs free energy curve is revealed in the present particular case of DAS domain growth controlled by one-by-one addition of single SF half-units. Acknowledgements This work has been supported by a Grant-in-Aid for Scientific Research ŽB. from the Ministry of Education, Science and Culture, Japan, and by a Research for the Future from the Japan Society for the Promotion of Science ŽJSPS.. References w1x K. Takayanagi, Y. Tanishiro, S. Takahashi, M. Takahashi, Surf. Sci. 164 Ž1985. 367. w2x K. Takayanagi, Y. Tanishiro, S. Takahashi, M. Takahashi, J. Vac. Sci. Technol. A 3 Ž1985. 1502. w3x R.S. Becker, J.A. Golovcheko, G.S. Higashi, B.S. Swartzentruber, Phys. Rev. Lett. 57 Ž1986. 1020. w4x T. Hoshino, K. Kokubun, K. Kumamoto, T. Ishimaru, I. Ohdomari, Jpn. J. Appl. Phys. 34 Ž1995. 3346. w5x N. Osakabe, K. Yagi, G. Honjo, Jpn. J. Appl. Phys. 19 Ž1980. L309. w6x W. Telieps, E. Bauer, Surf. Sci. 162 Ž1985. 163. w7x T. Hoshino, K. Kumamoto, K. Kokubun, T. Ishimaru, I. Ohdomari, Phys. Rev. B 51 Ž1995. 14594. w8x K. Kumamoto, T. Hoshino, K. Kokubun, T. Ishimaru, I. Ohdomari, Phys. Rev. B 53 Ž1996. 12907. w9x T. Hoshino, K. Kokubun, H. Fujiwara, K. Kumamoto, T. Ishimaru, I. Ohdomari, Phys. Rev. Lett. 75 Ž1995. 2372.
Stepwise change in Gibbs free energy curve observed in Si ž111 / DAS domain growth T. Ishimaru b
a,)
, K. Shimada a , T. Hoshino c , H. Kawada a , I. Ohdomari
a,b
a School of Science and Engineering, Waseda UniÕersity, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169, Japan Kagami Memorial Laboratory for Material Science and Technology, Waseda UniÕersity, 2-8-26 Nishiwaseda, Shinjuku-ku, Tokyo 169, Japan c Faculty of Pharmaceutical Sciences, Chiba UniÕersity, 1-33 Yayoicho, Inage-ku, Chiba 263, Japan
Received 1 September 1997; accepted 26 December 1997
Abstract The formation and the annihilation rates of stacking fault ŽSF. half-units were precisely determined from the high-temperature scanning tunneling microscopy ŽSTM. observation of dimer–adatom–stacking-fault ŽDAS. domains grown on quenched SiŽ111. surface at 4858C, as a function of the number of corner holes shared by a preexisting large domain and a newly born single SF triangle. In contrast to the general nucleation and growth with a single atom as a building unit, in the nucleation and growth of a n = n DAS domain with a single SF half-unit as a building unit, Gibbs free energy as a function of the number of SF half-units has discrete values. This feature is reflected in the behavior of a newly born SF half-unit adjacent to a larger DAS domain. For the SF half-units sharing one corner hole, the formation rate was lower than the annihilation rate due to the greater contribution of periphery strain to the increase in the Gibbs free energy than that of area increase. For the formation of the SF half-unit sharing two corner holes, the annihilation rate was negligibly small, suggesting that the addition of this single SF triangle increases the domain area keeping the periphery length constant, which results in Gibbs free energy reduction. q 1998 Elsevier Science B.V. All rights reserved. PACS: 68.35.Rh; 82.60.Nh; 64.60.Qb; 82.65.Dp Keywords: SiŽ111. surface; DAS domain; Nucleation and growth; Quantized Gibbs free energy change; Formation rate; Annihilation rate
1. Introduction SiŽ111. dimer–adatom–stacking-fault ŽDAS. reconstruction is one of the most interesting subjects in surface science. Not only the most stable 7 = 7 DAS structure but also the metastable n = n Ž n:odd. DAS structures with various sizes are known to appear on )
Corresponding author.
SiŽ111. surface w1–4x. The dynamical aspects of the DAS reconstruction have been extensively studied, and many features of the DAS domain growth have been made clear w5–8x. Our high-temperature scanning tunneling microscopy ŽSTM. observation of the quenched SiŽ111. surface has shown that the single stacking fault ŽSF. half-units appeared in the disordered ‘1 = 1’ region and the DAS domain growth proceeded by adding the SF half-units one by one
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 0 1 8 - X
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
sharing a corner hole w7,8x, which has revealed that the SF half-unit is a building unit of the DAS domain growth. We have been successful also to clarify the existence of the critical nucleus size of DAS domain growth and to determine the critical nucleus size at several temperatures w9x. The temperature dependence of the critical size were explained reasonably by the Gibbs free energy change based on a simple two-dimensional nucleation and growth theory. The Gibbs free energy curve for DAS domain nucleation can be understood by the competition between the energy decrease as a function of the DAS domain area and the energy increase as a function of the boundary length between ‘1 = 1’ matrix and DAS domain. In general for nucleation and growth, the Gibbs free energy changes smoothly as the domain size increases. This is because the atom size added to a preexisting domain is much smaller than the domain size. However, in the case of n = n DAS domain growth, the size of a single SF half-unit is not negligible compared to a domain size. This fact forces us to imagine that the Gibbs free energy curve cannot be continuous nor smooth because of the one-by-one addition of the building unit. In this work, through a very large number of sequential STM observation, we have obtained the formation and annihilation rates of the SF half-unit as a function of the number of corner holes shared by a preexisting large domain and a newly born SF triangle. The results clearly revealed the stepwise increase and decrease in the Gibbs free energy.
2. Experimental The experiments were performed using high-temperature STM unit ŽJEOL 4000XV. installed in an ultrahigh vacuum chamber with a base pressure below 8 = 10y1 1 Torr. A sample with a size of 7 = 1 = 0.3 mm3 was cut from a CZ wafer with the resistivity of 5 V cm and with the off angle of 0.18. After organic chemical cleaning and 5% HF treatment, the sample was installed into the vacuum chamber, degassed at 5008C for 12 h, and flashed up
19
to 12008C until the whole area of the surface was covered with 7 = 7 phase. In order to make high-temperature STM observation immediately after the quenching, the SiŽ111. surface was kept at the observation temperature of 4858C for over 1 h in advance using a dc current supply, then rapidly heated up to 11008C and rapidly cooled down again to 4858C using another dc current supply. The STM observations at 4858C were started just a few minutes after the quenching. The sample temperature of 4858C was determined by a power– temperature relationship based on the temperatures above 6008C measured by an infrared pyrometer. All STM images were acquired with a constant height mode and at a scan rate of 8.8 srimage, and were recorded on video tapes for over 3 h.
3. Results Fig. 1 shows the growth of DAS domains on the quenched SiŽ111. surface at 4858C. On the quenched surface kept at around 4858C, both the DAS region and the disordered ‘1 = 1’ region coexist, and the DAS domain growth is slow enough to see the formation of the individual SF half-unit. In the successive STM images in Fig. 1, the SF half-units indicated by the thick lines are the ones newly added to a side of a large DAS domain with sharing of one corner hole or two corner holes. It is also noted that a SF half-unit annihilated in Fig. 1h, i. In the following, the newly born SF half-unit sharing one Žtwo. corner holeŽs. with a preexisting large DAS domain is denoted by SF1 ŽSF2.. The frequency of the formation of SF1 and SF2 were counted from more than 1000 STM images, and the formation rate of each SF half-unit was determined by dividing the total number of formations of each SF half-unit by the total existence time of the available formation sites. The numbers of the annihilation of SF1 and SF2 were also counted, and the annihilation rate of each SF half-unit was determined by dividing the annihilation number by the total existence time of each SF half-unit. The formation and annihilation rates are summarized in Table 1 together with the number of formation and annihila-
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
20
Fig. 1. Successive STM images observed at around 4858C. The images of Žb. – Ži. were taken at 9, 18, 52, 70, 88, 106, 112 and 150 s after Ža., respectively. SF half-units indicated by thick lines are the newly formed one after the previous image. A SF half-unit sharing one corner hole annihilated in Ži..
tion in parentheses. What should be noted is, for SF1, that the formation rate is lower than the annihilation rate in spite of the supercooling condition for the DAS phase to grow. For SF2, namely in the
case where a single SF half-unit is added to a domain with sharing of two corner holes, the formation rate is reasonably high and the annihilation rates are negligibly small.
Table 1 Formation and annihilation rates of SF1 and SF2 Formation rate wsy1 x Žnumber of formation. SF1 SF2
y4
6.5 = 10 Ž147. 4.9 = 10y3 Ž226.
Annihilation rate wsy1 x Žnumber of annihilation. 1.6 = 10y3 Ž24. y Ž0.
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
21
4. Discussion In the regular case of crystal nucleation and growth, a monomer, i.e., a building unit, is an atom, and the addition of individual atoms to the nucleus cannot be seen. So, the free energy curve to describe the nucleation and growth, which is given by the summation of the energy increase due to periphery increase and the energy decrease due to area increase, is regarded to be continuous and smooth. It is also noted that the nucleus is regarded to preserve the equilibrium shape. In the case of the nucleation and growth of DAS region, a SF half-unit corresponds to a monomer. The DAS domain growth takes place discontinuously by adding the SF half-unit one by one. Fig. 2a schematically shows the growth of DAS domain preserving the equilibrium shape, which was the assumption in our previous work to explain the experimentally determined temperature dependence of critical nucleus size. Fig. 2b shows the intermediate growth stages between two adjacent DAS domains in equilibrium shape cited from in Fig. 2a. In the intermediate stages, firstly, SF1 is added to a side of the DAS domain, and then, SF2 is added along the side. The number of SF2s is higher for the larger domain size, while the number of SF1 is usually only one irrespective of the domain size. The change in Gibbs free energy upon the formation of SF1 and SF2 is considered as follows. The area increment of a DAS domain is considered to be same for both SF1 and SF2. The peripheral length of the DAS domain increases by 3a Ž a is one side length of a SF half-unit. upon SF1 formation, whereas the peripheral length does not change upon SF2
Fig. 2. Schematics of Ža. DAS domain growth preserving the equilibrium triangular shape, and Žb. intermediate growth stages between the triangular shaped DAS domains in the box in Ža.. In Žb., SF1 is first added to a side of the original DAS domain, and then SF2s are added along the side.
Fig. 3. Quantized Gibbs free energy curve upon the nucleation of DAS domain. It is based on the one-by-one addition of the SF half units. The lower line is the energy decrease due to the area increase, and the upper line is the energy increase due to the periphery increase. The arrows with 1–3 correspond to those in Fig. 2b.
formation. Hence, for SF1 formation, the Gibbs free energy should increase if the energy increase due to the periphery increase is larger than the energy decrease due to the area increase. On the other hand, for SF2 formation, the Gibbs free energy simply decreases as the area increases. Fig. 3 shows the Gibbs free energy change upon DAS domain nucleation and growth on the basis of the energy change associated with ‘1 = 1’™ 7 = 7 phase transition, the data of which was used in our previous work w9x. The lower line is the energy decrease due to the area increase of DAS domain which is proportional to the number of the SF halfunit newly added to the domain. The upper line is the energy increase due to the boundary strain, which increases only when the SF1 is added to a straight side of a domain. The growth stages indicated by the numbered arrows correspond to those in Fig. 2a. It is interesting to note that the free energy curve is discontinuous. It is obvious that, for a single SF triangle to be formed, an activation energy to put more than 50 atoms in order is necessary. Fig. 4 schematically shows the process of one-by-one addition of SF half-unit in terms of energy change. The process corresponds to the one in Fig. 2a and the horizontal lines correspond to the quantized free energy values shown in Fig. 3. D Ef1 and D Ef2 in Fig. 4 are the activation energy of the SF1 and SF2 formation, and D Ea1 and D Ea2 the activation energy for the SF1
22
T. Ishimaru et al.r Applied Surface Science 130–132 (1998) 18–22
Fig. 4. Schematic diagram of the formation and annihilation processes of the SF half-units. The numbers 1–3 correspond to those in Fig. 2b and Fig. 3. D Ef1 and D Ef2 are the activation energy for the SF1 and SF2 formation, and D Ea1 and D Ea2 are the activation energy for the SF1 and SF2 annihilation, respectively.
and SF2 annihilation, respectively. For SF1 formation, due to the higher frequency of annihilation based on smaller D Ea1 than D Ef1 , the annihilation rate is higher than the formation rate as seen in Table 1. For stages 2 and 3, D Ef2 is smaller than D Ea2 because of the free energy decrease, and therefore the formation rate becomes higher than the annihilation rate, in agreement with the experimental results. These local features of Gibbs free energy change is considered to be seen in every growth stage from a triangular DAS domain to the next larger triangular DAS domain.
5. Conclusion The formation and the annihilation rates of SF1 and SF2 were precisely determined from the hightemperature STM observation of the DAS domain growth on quenched SiŽ111. surface at 4858C. The local feature of the Gibbs free energy change upon the DAS domain nucleation was investigated. For the
SF half-unit formation sharing one corner hole, it was found from the lower formation rate and the annihilation rate that the Gibbs free energy increased. For the formation of the SF half-unit sharing two corner holes, the Gibbs free energy decreased, which qualitatively agrees with the result of the far smaller annihilation rate than the formation rate. It is concluded that the discrete and stepwise feature of the Gibbs free energy curve is revealed in the present particular case of DAS domain growth controlled by one-by-one addition of single SF half-units. Acknowledgements This work has been supported by a Grant-in-Aid for Scientific Research ŽB. from the Ministry of Education, Science and Culture, Japan, and by a Research for the Future from the Japan Society for the Promotion of Science ŽJSPS.. References w1x K. Takayanagi, Y. Tanishiro, S. Takahashi, M. Takahashi, Surf. Sci. 164 Ž1985. 367. w2x K. Takayanagi, Y. Tanishiro, S. Takahashi, M. Takahashi, J. Vac. Sci. Technol. A 3 Ž1985. 1502. w3x R.S. Becker, J.A. Golovcheko, G.S. Higashi, B.S. Swartzentruber, Phys. Rev. Lett. 57 Ž1986. 1020. w4x T. Hoshino, K. Kokubun, K. Kumamoto, T. Ishimaru, I. Ohdomari, Jpn. J. Appl. Phys. 34 Ž1995. 3346. w5x N. Osakabe, K. Yagi, G. Honjo, Jpn. J. Appl. Phys. 19 Ž1980. L309. w6x W. Telieps, E. Bauer, Surf. Sci. 162 Ž1985. 163. w7x T. Hoshino, K. Kumamoto, K. Kokubun, T. Ishimaru, I. Ohdomari, Phys. Rev. B 51 Ž1995. 14594. w8x K. Kumamoto, T. Hoshino, K. Kokubun, T. Ishimaru, I. Ohdomari, Phys. Rev. B 53 Ž1996. 12907. w9x T. Hoshino, K. Kokubun, H. Fujiwara, K. Kumamoto, T. Ishimaru, I. Ohdomari, Phys. Rev. Lett. 75 Ž1995. 2372.